ETC5543 Report - The conjBayes R package development
Pranali Angne, Student ID: 32355068
2022-11-13
1 Abstract
The aim of this internship was to develop a whole new package named conjBayes for the unit ETC4541/ETC5410, Bayesian inference and data analysis. The conjBayes packages provides functions for updating conjugate Bayesian prior distributions to the posterior distribution. All the functions have been specially formatted using the roxygen format above the source code for each function. Then these defined functions in this package have been added to the corresponding test files converting the existing unit tests cases to testthat format and increasing the code coverage of tests. During the process of developing conjBayes package, a few R packages were applied, including usethis, devtools, roxygen2, pkgdown, and testthat. I’ll be reviewing my work on the conjBayes package in this report. I discovered my weaknesses during the internship and got better at solving challenging issues when developing or upgrading R packages.
2 Background and motivation
The conjBayes is an R package designed to help students (understand) and apply Conjugate Bayesian models. The project my supervisor had in mind involves creating a package of R programs that she has written to do Markov chain Monte Carlo algorithms to fit various Bayesian statistical models. In particular my supervisor was looking for a package that do 1. Beta/ Binomial (Beta/ Bernoulli) 2. Gamma Exponential 3. Gamma/Poisson 4. Normal/Normal 5. Normal Inverse Gamma For all these we needed the pdf, cdf quantile function and the ability to sample random draws. She also wanted to have a vignettes. Therefore, my job was to help my supervisor develop the conjBayes package and help her converting the format of documentation and unit tests, as well as creating the vignette.
I believe that this internship gives me the chance to put my knowledge to use in a difficult, real-world setting. It might allow me to put my knowledge to use, identify my weaknesses, and enhance my capacity for handling challenging R-package issues.
Furthermore, Conjugate Bayesian prior distributions can be updated to the posterior distribution using the functions provided by the conjBayes package, because it was designed to help students (understand) and apply Conjugate Bayesian models and, I hope to help my supervisor to develop this package and provide it to more users. Overall, those are my motivations that joining the internship and working on developing the conjBayes package as this my first time working for a internship which built a lot of confidence and this will definitely help me for my future.
3 The development of the conjBayes package
The name of this package is conjBayes which offers “Functions for updating conjugate priors for Bayesian analysis”. Currently, the conjBayes is being developed to version 1.0.0. The author for this package is Dr. Catherine Forbes . The package conjBayes is an R package. The conjBayes packages provides functions for updating conjugate Bayesian prior distributions to the posterior distribution under GPL (>= 3) license.
I primarily assist my supervisor during the internship with increasing the number of unit tests, converting the original unit test cases format to the testthat format, and documenting functions using the roxygen format (or converting the original format to the roxygen format). I also assist with creating vignettes. While conjBayes is being developed, running the R-CMD-check, debugging, and submitting the modification to Github for reproducibility are also important and routine. Additionally, to build the package, the R-CMD-check, pkgdown, and test-coverage have all been posted to Github Actions.
3.1 Unit test format transformation
To carry out unit testing. The testthat package was used and create new unit tests for each of the six tested functions as the functions were being created. All the functions have been tested and they work perfectly fine.
3.2 Vignette of conjBayes package
There is a vignette of conjBayes in the version 1.0.0. My supervisor generated the function, therefore, I helped her to cretate a vignette/ directory, adding necessary dependencies to the description file and drafting the vignette. vignettes.
The vignette is made to make it easier for users to comprehend both how to use the package and its key features. Therefore, there are four sections the vignette that contain the explanation of the two most important functions in the conjBayes package: 1. Introduction 2. Gamma prior for Poisson data model 3. Beta prior for Bernoulli data model 4. and an example of Zombie Apocalypsein
- Introduction The initial section is the introductory section which explains The conjBayes packages provides functions for updating conjugate Bayesian prior distributions.
When data are modelled conditional on an unknown parameter, say \(\theta\), the marginal distribution assumed for \(\theta\) is known as the prior distribution and the posterior distribution is the conditional distribution for \(\theta\) given the observed data. This posterior distribution is determined by Bayes theorem. When the posterior distribution can be calculated in closed form, and belongs to the same distributional family as the prior distribution, then the prior is called a conjugate prior for the given data model.
Each conjBayes function reports the hyperparameters of the relevant prior distribution corresponding to the prior and model combination as indicated by the function name. Let’s look at an example to see how the functions work.
- Gamma prior for Poisson data model:
A part of the vignette is shown in Figure 3.1:
Figure 3.1: Vignette
For the Gamma prior for Poisson data model we considered the dataset discoveries, which contains the number of “great” inventions and scientific discoveries in each year of the 100 year period 1860 to 1959. And after updating the hyper parameters prior probabilities can be confirmed. We use the GammaPoisson function to update the Gamma distribution hyperparameters, given the data values in discoveries.
- Beta prior for Bernoulli data model:
Next section was about Beta prior for Bernoulli data model. Meanwhile, in the section introducing the BetaBernoulli function, a complete process including the trial design, data generation and data analysis has been created to guide users to apply this function. Besides, this section also explains three important arguments to help users better use the function to get the appropriate result. The application of the BetaBernoulli function is shown in Figure ??:
Figure 3.2: The Example of BetaBernoulli Function
- And the last is providing an example of the Zombie Apocalypsein:
A final (and fun!) example is described in the RPub “Fundamentals of Bayesian Data Analysis in [RPubs] (https://rpubs.com/klinares/443186). We want to know the probability we have found a vaccine to cure a zombie outbreak.
Below we use the code provided in the RPub to generate 13 vaccine outcomes, where a success corresponds to a cure.
Figure 3.3: Zombie Apocalypsein Example
Figure 3.4: The Example of Zombie Apocalypsein
Since we have 3 successes out of 13 independent trials, we can use the BetaBinomial function from the conjBayes package. This time let’s assume our prior is Beta(shape1 = 3, shape2 = 97), which corresponds to assuming the expected probability of success (that the zombie outbreak vaccine will work on any individual) is 0.03 and (before we see any data…) \(\Pr(p \leq\) 0.0822077 \()=0.99\). Then we have
Figure 3.5: Zombie example
4 Conclusion
In conclusion, updating a package is a complicated job, especially when we need to develop it from scratch. However, this is also a good opportunity for me to apply my learning and practice my knowledge, as well as learn some new knowledge. Besides, resolving the errors and the debugging process was quite interesting to learn. I will say I could learn the most out of the internship and extremely thankful towards my supervisor who is so much patient with abundance of knowledge and provided me with first hand experience through her work.
Overall, this is a good opportunity for me and I think it could help my future career. Lastly I would like to thank Monash Universty especially prof. Di Cook and Prof. Rob Hyndman who gave me an opportunity by providing me this internship.